Classical dynamical localization

Abstract

We consider classical models of the kicked rotor type, with piecewise linear kicking potentials designed so that momentum changes only by multiples of a given constant. Their dynamics display quasi-localization of momentum, or quadratic growth of energy, depending on the arithmetic nature of the constant. Such purely classical features mimic paradigmatic features of the {\it quantum} kicked rotor, notably dynamical localization in momentum, or quantum resonances. We present a heuristic explanation, based on a classical phase space generalization of a well known argument, that maps the quantum kicked rotor on a tight-binding model with disorder. Such results suggest reconsideration of generally accepted views, that dynamical localization and quantum resonances are a pure result of quantum coherence.

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• Floquet states of kicked particle in a singular potential: Exponential and power-law profiles
• Bloch theorem dictated wave chaos in microcavity crystals
• Logarithmic expansion of many-body wave packets in random potentials
• Coexistence of Anderson Localization and Quantum Scarring in Two Dimensions
• Records and occupation time statistics for area-preserving maps